An Examination of Transformation Techniques to Investigate and Interpret Multivariate Geochemical Data Analysis: Tellus Case Study

This research aims to use the multivariate geochemical dataset, generated by the Tellus project, to investigate the appropriate use of transformation methods to maintain the integrity of geochemical data and inherent constrained behaviour in multivariate relationships. The widely used normal score transform is compared with the use of a stepwise conditional transform technique. The Tellus Project, managed by GSNI and funded by the Department of Enterprise Trade and Development and the EU’s Building Sustainable Prosperity Fund, involves the most comprehensive geological mapping project ever undertaken in Northern Ireland. Previous study has demonstrated spatial variability in the Tellus data but geostatistical analysis and interpretation of the datasets requires use of an appropriate methodology that reproduces the inherently complex multivariate relations. Previous investigation of the Tellus geochemical data has included use of Gaussian-based techniques. However, earth science variables are rarely Gaussian, hence transformation of data is integral to the approach. The multivariate geochemical dataset generated by the Tellus project provides an opportunity to investigate the appropriate use of transformation methods, as required for Gaussian-based geostatistical analysis. In particular, the stepwise conditional transform is investigated and developed for the geochemical datasets obtained as part of the Tellus project. The transform is applied to four variables in a bivariate nested fashion due to the limited availability of data. Simulation of these transformed variables is then carried out, along with a corresponding back transformation to original units. Results show that the stepwise transform is successful in reproducing both univariate statistics and the complex bivariate relations exhibited by the data. Greater fidelity to multivariate relationships will improve uncertainty models, which are required for consequent geological, environmental and economic inferences.

Compositional Data Analysis in Forensic Geoscience

Statistics are regularly used to make some form of comparison between trace evidence or deploy the exclusionary principle (Morgan and Bull, 2007) in forensic investigations. Trace evidence are routinely the results of particle size, chemical or modal analyses and as such constitute compositional data. The issue is that compositional data including percentages, parts per million etc. only carry relative information. This may be problematic where a comparison of percentages and other constraint/closed data is deemed a statistically valid and appropriate way to present trace evidence in a court of law. Notwithstanding an awareness of the existence of the constant sum problem since the seminal works of Pearson (1896) and Chayes (1960) and the introduction of the application of log-ratio techniques (Aitchison, 1986; Pawlowsky-Glahn and Egozcue, 2001; Pawlowsky-Glahn and Buccianti, 2011; Tolosana-Delgado and van den Boogaart, 2013) the problem that a constant sum destroys the potential independence of variances and covariances required for correlation regression analysis and empirical multivariate methods (principal component analysis, cluster analysis, discriminant analysis, canonical correlation) is all too often not acknowledged in the statistical treatment of trace evidence. Yet the need for a robust treatment of forensic trace evidence analyses is obvious. This research examines the issues and potential pitfalls for forensic investigators if the constant sum constraint is ignored in the analysis and presentation of forensic trace evidence. Forensic case studies involving particle size and mineral analyses as trace evidence are used to demonstrate the use of a compositional data approach using a centred log-ratio (clr) transformation and multivariate statistical analyses.

Compositional data analysis of Holocene sediments from the West Bengal Sundarbans, India: Geochemical proxies for grain-size variability in a delta environment

This paper is part of a special issue of Applied Geochemistry focusing on reliable applications of compositional multivariate statistical methods. This study outlines the application of compositional data analysis (CoDa) to calibration of geochemical data and multivariate statistical modelling of geochemistry and grain-size data from a set of Holocene sedimentary cores from the Ganges-Brahmaputra (G-B) delta. Over the last two decades, understanding near-continuous records of sedimentary sequences has required the use of core-scanning X-ray fluorescence (XRF) spectrometry, for both terrestrial and marine sedimentary sequences. Initial XRF data are generally unusable in ‘raw-format’, requiring data processing in order to remove instrument bias, as well as informed sequence interpretation. The applicability of these conventional calibration equations to core-scanning XRF data are further limited by the constraints posed by unknown measurement geometry and specimen homogeneity, as well as matrix effects. Log-ratio based calibration schemes have been developed and applied to clastic sedimentary sequences focusing mainly on energy dispersive-XRF (ED-XRF) core-scanning. This study has applied high resolution core-scanning XRF to Holocene sedimentary sequences from the tidal-dominated Indian Sundarbans, (Ganges-Brahmaputra delta plain). The Log-Ratio Calibration Equation (LRCE) was applied to a sub-set of core-scan and conventional ED-XRF data to quantify elemental composition. This provides a robust calibration scheme using reduced major axis regression of log-ratio transformed geochemical data. Through partial least squares (PLS) modelling of geochemical and grain-size data, it is possible to derive robust proxy information for the Sundarbans depositional environment. The application of these techniques to Holocene sedimentary data offers an improved methodological framework for unravelling Holocene sedimentation patterns.

Multivariate Statistical Analysis Applied to an IL6 Signal Transduction Model in Hepatocytes

This paper introduces the application of linear multivariate statistical techniques, including partial least squares (PLS), canonical correlation analysis (CCA) and reduced rank regression (RRR), into the area of Systems Biology. This new approach aims to extract the important proteins embedded in complex signal transduction pathway models.The analysis is performed on a model of intracellular signalling along the janus-associated kinases/signal transducers and transcription factors (JAK/STAT) and mitogen activated protein kinases (MAPK) signal transduction pathways in interleukin-6 (IL6) stimulated hepatocytes, which produce signal transducer and activator of transcription factor 3 (STAT3).A region of redundancy within the MAPK pathway that does not affect the STAT3 transcription was identified using CCA. This is the core finding of this analysis and cannot be obtained by inspecting the model by eye. In addition, RRR was found to isolate terms that do not significantly contribute to changes in protein concentrations, while the application of PLS does not provide such a detailed picture by virtue of its construction.This analysis has a similar objective to conventional model reduction techniques with the advantage of maintaining the meaning of the states prior to and after the reduction process. A significant model reduction is performed, with a marginal loss in accuracy, offering a more concise model while maintaining the main influencing factors on the STAT3 transcription.The findings offer a deeper understanding of the reaction terms involved, confirm the relevance of several proteins to the production of Acute Phase Proteins and complement existing findings regarding cross-talk between the two signalling pathways.

A three-position spectral line survey of sagittarius B2 between 218 and 263 GHz. II. Data analysis

We present an analysis of the data from our Swedish-ESO Submillimetre Telescope molecular line survey in the 1.3 mm band of the N, M, and NW positions in the Sgr B2 molecular cloud. The line emissions from 42 molecular species, and some of their isotopomers, were analyzed assuming a single temperature and a homogeneous source. In cases where a source size much smaller than the antenna beam (23

Time of flight mass spectrometry for quantitative data analysis in fast transient studies using a Temporal Analysis of Products (TAP) reactor

A Time of flight (ToF) mass spectrometer suitable in terms of sensitivity, detector response and time resolution, for application in fast transient Temporal Analysis of Products (TAP) kinetic catalyst characterization is reported. Technical difficulties associated with such application as well as the solutions implemented in terms of adaptations of the ToF apparatus are discussed. The performance of the ToF was validated and the full linearity of the specific detector over the full dynamic range was explored in order to ensure its applicability for the TAP application. The reported TAP-ToF setup is the first system that achieves the high level of sensitivity allowing monitoring of the full 0-200 AMU range simultaneously with sub-millisecond time resolution. In this new setup, the high sensitivity allows the use of low intensity pulses ensuring that transport through the reactor occurs in the Knudsen diffusion regime and that the data can, therefore, be fully analysed using the reported theoretical TAP models and data processing.